UVALive - 4960 Sensor network(生成树+LCA)

题目大意：给出N个点。M条边。问这N个点形成的生成树的最大权值边-最小权值边的最小值

解题思路：先排序，然后按生成树的kruscal算法进行加边，再维护一个最小权值边

加边的时候要考虑一下加下去的边是否会形成环，假设形成环的话，就把环内的最小边去掉，然后再找出这棵新的生成树的最小边

等到生成树形成的时候，由于加入进去的新边的权值肯定是最大值的，所以仅仅要仅仅减去之前维护一个的最小值就能够了

#include <cstdio>
#include <cstring>
#include <algorithm>
#include <vector>
using namespace std;

#define N 400
#define M 160010
#define INF 0x3f3f3f3f

struct Edge{
    int u, v, c;
    Edge() {}
    Edge(int u, int v, int c): u(u), v(v), c(c) {}
}E[M];

int f[N], dis[N][N];
int cnt, Min_Edge, n, m;
bool vis[N];

int cmp(const Edge &a, const Edge &b) {
    return a.c < b.c;
}

void init() {
    for (int i = 0; i < m; i++) {
        scanf("%d%d%d", &E[i].u, &E[i].v, &E[i].c);
        dis[E[i].u][E[i].v] = dis[E[i].v][E[i].u] = E[i].c;
    }
}

int LCA(int i) {
    int u = E[i].u, v = E[i].v, c = E[i].c;
    memset(vis, 0, sizeof(vis));
    while (!vis[u]) {
        vis[u] = true;
        if (u == f[u]) break;
        u = f[u];
    }

    while (!vis[v] && f[v] != v) v = f[v];
    if (!vis[v]) return -1;
    return v;
}

void findCycle(int i) {
    int lca = LCA(i);
    if (lca == -1) return ;
    int u = E[i].u, v = E[i].v, c = E[i].c;
    Edge MinEdge;
    MinEdge.c = INF;
    int fu = f[u];
    while (fu != u && u != lca) {
        if (dis[fu][u] < MinEdge.c) MinEdge = Edge(fu, u, dis[fu][u]);

        fu = f[fu];
        u = f[u];

    }

    int fv = f[v];
    while (fv != v && v != lca) {
        if (dis[fv][v] < MinEdge.c) MinEdge = Edge(fv, v, dis[fv][v]);
        fv = f[fv];
        v = f[v];
    }

    f[MinEdge.v] = MinEdge.v;
    Min_Edge = INF;
    for (int i = 0; i < n; i++)
        if (f[i] != i && dis[f[i]][i] < Min_Edge)
            Min_Edge = dis[f[i]][i];
    cnt--;
}

void AddEdge(int i) {
    int u = E[i].u, v = E[i].v, c = E[i].c;
    if (f[u] == u) f[u] = v;
    else if (f[v] == v) f[v] = u;
    else {
        vector<int> vec;
        while (1) {
            vec.push_back(u);
            if (u == f[u]) break;
            u = f[u];
        }
        int size = vec.size();
        for (int i = size - 1; i > 0; i--) f[vec[i]] = vec[i - 1];
        f[E[i].u] = E[i].v;
    }
    Min_Edge = min(Min_Edge, c);
    cnt++;
}

void solve() {
    sort(E, E + m, cmp);
    for (int i = 0; i < n; i++)
        f[i] = i;

    int ans = INF;
    Min_Edge = INF;
    cnt = 0;
    for (int i = 0; i < m; i++) {
        findCycle(i);
        AddEdge(i);
        if (cnt == n - 1) ans = min(ans, E[i].c - Min_Edge);

    }
    printf("%d\n", ans);
}

int main() {
    while (scanf("%d", &n) != EOF && n) {
        scanf("%d", &m);
        init();
        solve();
    }
    return 0;
}